We consider a semi-classical Schrödinger operator -h2Δ + V with a degenerate potential V(x, y) = f(x)g(y). g is assumed to be a homogeneous positive function of m variables and f is a strictly positive function of n variables, with a strict minimum. We give sharp asymptotic behavior of low eigenvalues bounded by some power of the parameter h, by improving Born-Oppenheimer approximation.
@article{1589,
title = {Accuracy on eigenvalues for a Schr\"odinger operator with a degenerate potential in the semi-classical limit},
journal = {CUBO, A Mathematical Journal},
volume = {9},
year = {2007},
language = {en},
url = {http://dml.mathdoc.fr/item/1589}
}
Morame, Abderemane; Truc, Françoise. Accuracy on eigenvalues for a Schrödinger operator with a degenerate potential in the semi-classical limit. CUBO, A Mathematical Journal, Tome 9 (2007) . http://gdmltest.u-ga.fr/item/1589/